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Automatic Control System .pdf

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Title: Automatic Control Systems, 9th Edition

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Ninth Edition

Farid Golnaraghi • Benjamin C. Kuo

Laplace Transform Table
Laplace Transform F(s)

Time Function f(t)


Unit-impulse function 8{t)


Unit-step function Us{i)


Unit-ramp function t

f(n = positive integer)




i' + Q!




(s + a)2
(s + a)" + 1
(s + a)(s + p)
(s + a)(s + p)

t"e~°"(n = positive integer)



s(s + a)

5(5 + a ) 2

i ( l - e~at or

s2 (s + a)

s (s + a)
(s + a)2




){a J 0


+ e-m)









s + col
s +co2

sin co„t

Laplace Transform Table (cont.)

Time Function /(7)

Laplace Transform F(s)



1 — cos cont

s{s +co )
con J a2 + OJ2 sin(6>„/ + 9)
where 6 = t a n - ' (con/a)
" r-°" 1
nnf/.t t
<* + «5
\/ff2 + co2


(5 + a) (j2 + ^ 2 )


w h e r e # = t a n - (co„/a)
J 2 + 2t;cons + co2






v-2 »








C '


?-&"'<\«{„hl^f\ & t +a)

s{s + 2t;cons + co )
wherefl^cos""" 1 ?





s2 + 2£co„s + co2

r"to"'nnfa) \/l


wherefl = cos~ l £

s2(s2 + 2^cons + co2)


• W " " f ^ " ^ * ^ " " * ^ ^ 1 -f 2 , + ")


where* - tan" 1 ^




/ 2

coj,{s + a)
s2 + 2$co„s + a>2

f2 f

O j-


1 ^
a - £con




t - ^ +
? ' - * * s m ( w „ \ / l - <2 / + 0)
«h tony/I-^
where# = c o s ( 2 £ - l )

Automatic Control
Simon Fraser University

University of Illinois at Urbana-Champaign


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To order books or for customer service, please call 1-800-CALL WILEY (225-5945).
MATLAB* and Simullnk* are trademarks of The MathWorks. Inc. and are used with permission. The
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MATIAB* software or related products does not constitute endorsement or sponsorship hy The MathWorks
of a particular pedagogical approach or particular use of the MATLAB software.

ISBN-13 978-0470-04896-2
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1

To my wife, Mitra, and to Sophia and Carmen, the joys of my life.
—M. Farid Golnaraghi

Preface (Readme)
This is the ninth edition of the text but the first with Farid Golnaraghi as the lead author.
For this edition, we increased the number of examples, added MATLAB'" ' toolboxes, and
enhanced the MATLAB GUI software, ACSYS. We added more computer-aided tools for
students and teachers. The prepublication manuscript was reviewed by many professors,
and most of the relevant suggestions have been adopted. In this edition, Chapters 1 through
4 are organized to contain all background material, while Chapters 5 through 10 contain
material directly related to the subject of control.
In this edition, the following materials have been moved into appendices on this book's
Web site at www.wiley.com/college/golnaraghi.

A: Elementary Matrix Theory and Algebra
B: Difference Equations
C: Laplace Transform Table
D: z-Transform Table
E: Properties and Construction of the Root Loci
F: General Nyquist Criterion
G: ACSYS 2008: Description of the Software
H: Discrete-Data Control Systems

In addition, the Web site contains the MATLAB files for ACSYS, which are software
tools for solving control-system problems, and PowerPoint files for the illustrations in the
The following paragraphs are aimed at three groups: professors who have adopted the
book or who we hope will select it as their text; practicing engineers looking for answers to
solve their day-to-day design problems; and, finally, students who are going to live with the
book because it has been assigned for the control-systems course they are taking.
To the Professor: The material assembled in this book is an outgrowth of senior-level
control-system courses taught by the authors at their universities throughout their teaching
careers. The first eight editions have been adopted by hundreds of universities in the United
States and around the world and have been translated into at least six languages. Practically
all the design topics presented in the eighth edition have been retained.
This text contains not only conventional MATLAB toolboxes, where students can
learn MATLAB and utilize their programming skills, but also a graphical MATLAB-based
software, ACSYS. The ACSYS software added to this edition is very different from the
software accompanying any other control book. Here, through extensive use of MATLAB
GUI programming, we have created software that is easy to use. As a result, students will
need to focus only on learning control problems, not programming! We also have added
two new applications, SIMLab and Virtual Lab, through which students work on realistic
problems and conduct speed and position control labs in a software environment. In
SIMLab, students have access to the system parameters and can alter them (as in any
simulation). In Virtual Lab, we have introduced a black-box approach in which the students


MATLAB " is a registered trademark of The Math Works. Inc.



have no access to the plant parameters and have to use some sort of system identification
technique to find them. Through Virtual Lab we have essentially provided students with a
realistic online lab with all the problems they would encounter in a real speed- or positioncontrol lab—for example, amplifier saturation, noise, and nonlinearity. We welcome your
ideas for the future editions of this book.
Finally, a sample section-by-section for a one-semester course is given in the
Instructor's Manual, which is available from the publisher to qualified instructors. The
Manual also contains detailed solutions to all the problems in the book.
To Practicing Engineers: This book was written with the readers in mind and is very
suitable for self-study. Our objective was to treat subjects clearly and thoroughly. The book
does not use the theorem-proof-Q.E.D. style and is without heavy mathematics. The
authors have consulted extensively for wide sectors of the industry for many years and have
participated in solving numerous control-systems problems, from aerospace systems to
industrial controls, automotive controls, and control of computer peripherals. Although it is
difficult to adopt all the details and realism of practical problems in a textbook at this level,
some examples and problems reflect simplified versions of real-life systems.
To Students: You have had it now that you have signed up for this course and your
professor has assigned this book! You had no say about the choice, though you can form
and express your opinion on the book after reading it. Worse yet, one of the reasons that
your professor made the selection is because he or she intends to make you work hard. But
please don't misunderstand us: what we really mean is that, though this is an easy book to
study (in our opinion), it is a no-nonsense book. It doesn't have cartoons or nice-looking
photographs to amuse you. From here on, it is all business and hard work. You should have
had the prerequisites on subjects found in a typical linear-systems course, such as how to
solve linear ordinary differential equations, Laplace transform and applications, and timeresponse and frequency-domain analysis of linear systems. In this book you will not find
too much new mathematics to which you have not been exposed before. What is interesting
and challenging is that you are going to learn how to apply some of the mathematics that
you have acquired during the past two or three years of study in college. In case you need to
review some of the mathematical foundations, you can find them in the appendices on this
book's Web site. The Web site also contains lots of other goodies, including the ACSYS
software, which is GUI software that uses MATLAB-based programs for solving linear
control systems problems. You will also find the Simulink"12-based SIMLab and Virtual
Lab, which will help you to gain understanding of real-world control systems.
This book has numerous illustrative examples. Some of these are deliberately simple
for the purpose of illustrating new ideas and subject matter. Some examples are more
elaborate, in order to bring the practical world closer to you. Furthermore, the objective of
this book is to present a complex subject in a clear and thorough way. One of the important
learning strategies for you as a student is not to rely strictly on the textbook assigned. When
studying a certain subject, go to the library and check out a few similar texts to see how
other authors treat the same subject. You may gain new perspectives on the subject and
discover that one author may treat the material with more care and thoroughness than the
others. Do not be distracted by written-down coverage with oversimplified examples. The
minute you step into the real world, you will face the design of control systems with
nonlinearities and/or time-varying elements as well as orders that can boggle your mind. It


Simulink'1* is a registered trademark of The Math Works, Inc.

may be discouraging to tell you now that strictly linear and first-order systems do not exist
in the real world.
Some advanced engineering students in college do not believe that the material they
learn in the classroom is ever going to be applied directly in industry. Some of our students
come back from field and interview trips totally surprised to find that the material they
learned in courses on control systems is actually being used in industry today. They are
surprised to find that this book is also a popular reference for practicing engineers.
Unfortunately, these fact-finding, eye-opening, and self-motivating trips usually occur near
the end of their college days, which is often too late for students to get motivated.
There are many learning aids available to you: the MATLAB-based ACSYS software
will assist you in solving all kinds of control-systems problems. The SIMLab and Virtual
Lab software can be used for simulation of virtual experimental systems. These are all
found on the Web site. In addition, the Review Questions and Summaries at the end of each
chapter should be useful to you. Also on the Web site, you will find the errata and other
supplemental material.
We hope that you will enjoy this book. It will represent another major textbook
acquisition (investment) in your college career. Our advice to you is not to sell it back to the
bookstore at the end of the semester. If you do so but find out later in your professional
career that you need to refer to a control systems book, you will have to buy it again at a
higher price.


Special Acknowledgments: The authors wish to thank the reviewers for their invaluable
comments and suggestions. The prepublication reviews have had a great impact on the
revision project.
Dr. Earl Foster, Dr. Vahe Caliskan,
The authors thank Simon Fraser students and research associates Michael Ages,
Johannes Minor, Linda^Franak, Arash Jamalian, Jennifer Leone, Neda Parnian, Sean
MacPherson, Amin Kamalzadeh, and Nathan (Wuyang) Zheng for their help. Farid
Golnaraghi also wishes to thank Professor Benjamin Kuo for sharing the pleasure of
writing this wonderful book, and for his teachings, patience, and support throughout this
M. F. Golnaraghi,
Vancouver, British Columbia,
B. C. Kuo,
Champaign, Illinois, U.S.A.

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